The recent government shutdown may have distracted some Americans from the bungled rollout of Obamacare, but a new Pew survey shows many people are well aware of just how bad things are for the law’s new insurance websites. Forty-six percent of Americans polled on Oct. 9 to 13, while the shutdown was in full swing, said the Affordable Care Act’s online insurance exchanges were working “not too well” or “not working at all.”

While about 41% of Americans approve of the ACA, according to Pew, negative public perception of the exchanges could hinder the administration’s plan to enroll 7 million people in private health plans through the exchanges by the end of 2014. Before the error-riddled launch on Oct. 1, the White House promised the exchanges would be easy-to-use tools, allowing consumers to compare and buy insurance policies in the same way they book travel or buy books online. The harder the exchange websites are to use — or the harder consumers think they are to use — the less likely people are to log on or sign up. These persistent problems mean many of those who have enrolled so far have done so only after making multiple attempts to navigate slow and crash-prone websites.

While President Obama sought to reassure the public in a speech on Monday that exchange-website malfunctions were being fixed, a separate poll found that many believe technical problems plaguing the websites may indicate that the entire law is broken. A Washington Post–ABC News poll conducted Oct 17 to 20 and released Oct. 21 found that 56% of those surveyed believed the “website glitches” are “part of a broader problem with the health care law.”

This comes as some congressional Republicans have called for the resignation of the woman in charge of the rollout, Health and Human Services Secretary Kathleen Sebelius. The White House has said it stands by her. Even some White House allies, including former Obama press secretary Robert Gibbs, have said firings would be an appropriate response in the wake of the botched rollout. After wrangling over dates, Sebelius agreed to testify about the exchanges before the House Energy and Commerce Committee on Oct. 30.

The Administration has tried to head off panic about the law’s faulty start, acknowledging in a recent blog post that the federal exchange website “has not lived up to the expectations of the American people” and promising to bring in outside information-technology experts to address technical problems. But even the efforts of what Obama termed a “tech surge” will take some time to work. The President acknowledged as much in his speech when he urged those having trouble signing up online to call a federal hotline or visit designated community centers and hospitals to apply in person.

Yet, even if federal and state exchanges were all functioning properly, a third poll found that many Americans the administration hopes will use them do not understand how the marketplaces work. A recent Gallup poll shows that about 70% of uninsured Americans are unfamiliar with the exchanges, where they may be able to enroll in new coverage and access federal subsidies to make policies more affordable. This figure was essentially unchanged from September, before the exchanges launched. Awareness did rise among the general public, according to the Pew survey, with 65% of Americans aware of the existence of the exchanges, up from 51% in September.

The White House says some 20 million people have visited HealthCare.gov, the troubled federal exchange website, since it launched on Oct. 1. But those visits may not portend a future wave of enrollment. Although Pew found 1 in 7 Americans has visited an exchange website, more than half of those visitors already have insurance through an employer or government program, making them ineligible for new private coverage through Obamacare. About one-third of exchange website visitors were uninsured, according to Pew.